HMMT 十一月 2015 · GEN 赛 · 第 4 题
HMMT November 2015 — GEN Round — Problem 4
题目详情
- Chords AB and CD of a circle are perpendicular and intersect at a point P . If AP = 6 , BP = 12, and CD = 22, find the area of the circle.
解析
- Chords AB and CD of a circle are perpendicular and intersect at a point P . If AP = 6 , BP = 12, and CD = 22, find the area of the circle. Proposed by: Sam Korsky Answer: 130 π Let O be the center of the circle and let M be the midpoint of segment AB and let N be the midpoint of segment CD . Since quadrilateral OM P N is a rectangle we have that ON = M P = AM − AP = 3 so √ √ √ 2 2 OC = ON + N C = 9 + 121 = 130 Hence the desired area is 130 π .